The computational results show that the second-order methods with the rank-increasing strategy
do not have a good performance on this task. Thus,
we only present the results for the first-order methods under different sizes of sampling set \(\Omega \)  in Table REF . As in [1]}, the relative test error on a randomly sampling set \(\Gamma \)  (outside of \(\Omega \) ) with \(|\Gamma |=100\)  is reported, which is defined by \(\frac{\left\Vert  {\cal P}_{\Gamma }\left({\cal X}_t\right)- {\cal P}_{\Gamma }\left({\cal T}\right)\right\Vert _{{\footnotesize {\mathsf {F}}}}}{\left\Vert   {\cal P}_{\Gamma }\left({\cal T}\right)\right\Vert _{{\footnotesize {\mathsf {F}}}}}\) . From the table, we can see that all the four algorithms achieve the overall similar performance.
<TABLE>